The number 2017 can be expressed as the difference of the squares of two consecutive whole numbers. What is the sum of these two numbers?

Question

Mathematics

Ayla Werner

19 May, 10:55

The number 2017 can be expressed as the difference of the squares of two consecutive whole numbers. What is the sum of these two numbers?

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Answers (1)

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Noodles · Answer 1

Let x be the first number

X + 1 be the second number

So

(x+1) ^2 - x^2 = 2017

X^2 + 2x + 1 - x^2 = 2017

2x + 1 = 2017

2x = 2017 - 1

2x = 2016

X = 1008

X + 1 = 1009

Sum = 1008 + 1009 = 2017